

A304162


a(n) = n^4  3*n^3 + 9*n^2  7*n + 5 (n>=1).


1



5, 19, 65, 185, 445, 935, 1769, 3085, 5045, 7835, 11665, 16769, 23405, 31855, 42425, 55445, 71269, 90275, 112865, 139465, 170525, 206519, 247945, 295325, 349205, 410155, 478769, 555665, 641485, 736895, 842585, 959269, 1087685, 1228595, 1382785
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OFFSET

1,1


COMMENTS

For n>=2, a(n) is the second Zagreb index of the graph KK_n, defined as 2 copies of the complete graph K_n, with one vertex from one copy joined to two vertices of the other copy (see the Stevanovic et al. reference, p. 396).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The Mpolynomial of KK_n is M(KK_n; x,y) = (n2)^2*x^(n1)*y^(n1) + 2*(n2)*x^(n1)*y^n + (n1)*x^(n1)*y^(n+1) + x^n*y^n + 2*x^n*y^(n+1).


LINKS



FORMULA

G.f.: x*(5  6*x + 20*x^2 + 5*x^4) / (1  x)^5.
a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) for n>5.
(End)


MAPLE

seq(n^43*n^3+9*n^27*n+5, n = 1 .. 40);


MATHEMATICA

Table[n (n  1) (n^2  2 n + 7) + 5, {n, 1, 40}] (* Bruno Berselli, May 10 2018 *)


PROG

(PARI) Vec(x*(5  6*x + 20*x^2 + 5*x^4) / (1  x)^5 + O(x^60)) \\ Colin Barker, May 10 2018
(GAP) List([1..40], n>n^43*n^3+9*n^27*n+5); # Muniru A Asiru, May 10 2018


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



